They could put it on a payment plan or something
Very true. But here's the problem. It should take a doctor maybe 30 minutes to clean the carpenter's wound, then stitch it up.
So you've got to pay the doctor for 30 minutes of his time, plus you've got to pay for the assisting nurse. And you've got to pay the ER itself for 30 minutes of overhead.
In a sane world, that bill should come to around $300 or so. But I'll bet the bill would be $1000 or more. No attempt at fairness there.